To calculate the monthly payment for a loan, we can use the formula for calculating the monthly payment on a fixed-rate loan:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal loan amount
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments
In this case, the principal loan amount is $10,000, the annual interest rate is 6%, and the loan term is 5 years (60 months). Let's calculate the monthly payment:
r = 6% / 12 = 0.005 (monthly interest rate)
n = 60 (total number of monthly payments)
M = 10000 * (0.005 * (1 + 0.005)^60) / ((1 + 0.005)^60 - 1)
Calculating this, the monthly payment comes out to be approximately $193.33.
To calculate the total interest paid on the loan, we can subtract the principal loan amount from the total amount paid over the loan term. The total amount paid can be calculated by multiplying the monthly payment by the total number of monthly payments:
Total amount paid = M * n
Total interest paid = Total amount paid - Principal loan amount
Let's calculate the total interest paid:
Total amount paid = 193.33 * 60 = $11,599.80
Total interest paid = 11,599.80 - 10,000 = $1,599.80
So, the monthly payment for a $10,000 loan at 6% APR over 5 years is approximately $193.33, and the total interest paid on this loan is approximately $1,599.80.